Mechanical Engineering Principles

280 MECHANICAL ENGINEERING PRINCIPLES

Formula Formula symbols Units

Angular velocity ω=

θ

t

= 2 πn rad/s

Linear acceleration a=rα m/s^2

Relationships between initial velocityu, final velocity
v, displacements, timetand constant accelerationa

⎧

⎨

⎩

v 2 =v 1 +at

s=ut+^12 at^2

v^2 =u^2 + 2 as

m/s

m

(m/s)^2

Relationships between initial angular
velocity ω 1 , final angular velocity ω 2 ,
angleθ, timet and angular accelerationa

⎧

⎨

⎩

ω 2 =ω 1 +αt

θ=ω 1 t+^12 αt^2

ω 22 =ω^21 + 2 αθ

rad/s

rad

(rad/s)^2

Momentum = mass ×velocity kg m/s

Impulse=applied force×time=change in momentum kg m/s

Force = mass×acceleration F=ma N

Weight = mass×gravitational field W=mg N

Centripetal acceleration a=

v^2

r

m/s^2

Centripetal force F=

mv^2

r

N

Density =

mass

volume

ρ=

m

V

kg/m^3

Work done = force×distance moved W=Fs J

Efficiency =

useful output energy

input energy

Power=

energy used(or work done)

time taken

=force×velocity

P=

E

t

=Fv W

Potential energy=weight×change in height Ep=mgh J

kinetic energy =^12 ×mass×(speed)^2 Ek=^12 mv^2 J

kinetic energy of rotation

=^12 ×moment of inertia×(angular velocity)^2 Ek=^12 Iω^2

J

Frictional force=coefficient of friction×normal force F=μN N

Angle of repose,θ, on an inclined plane tanθ=μ

Efficiency of screw jack η=

tanθ

tan(λ+θ)

SHM periodic timeT = 2 π

√

displacement

acceleration

T= 2 π

√

y

a

s

T = 2 π

√

mass

stiffness

T= 2 π

√

m

k

s

simple pendulum T= 2 π

√

L

g

s